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Finite difference method for simulating phonon heat transport process. (Chinese. English summary) Zbl 1449.80026

Summary: The equation of phonon radiative transfer is a differential-integral equation. The finite difference method is used to numerically solve the equation of phonon radiative transfer with boundary conditions. The Gauss-Seidel method and the finite difference discretization can be used to ensure stable numerical solutions. Through an one-dimensional numerical simulation of the phonon heat transport process of Ge/Si/Ge film at room temperature and using the diffuse mismatch interface model at the interface, we can evaluate the influence of the temperature along the normal direction of the film and the thickness ratio of the Ge/Si film and the temperature jump at the interface on the thermal conductivity of the overal-1 structure of the material, and estimate the change of the thermal conductivity of the film as the thickness of the film increases. Through a two-dimensional numerical simulation of the phonon heat transport process of the silicon film, we can obtain the temperature along the normal and orientation-oriented distribution of the film, and the change in temperature and the thermal conductivity when the film width and thickness ratio are different.

MSC:

80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
80A21 Radiative heat transfer
35R09 Integro-partial differential equations
65F10 Iterative numerical methods for linear systems
74K35 Thin films
74F05 Thermal effects in solid mechanics